Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 20}$ ${-5x+3y = -34}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $2$ ${-6x-6y = -60}$ $-10x+6y = -68$ Add the top and bottom equations together. $-16x = -128$ $\dfrac{-16x}{{-16}} = \dfrac{-128}{{-16}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {2x+2y = 20}\thinspace$ to find $y$ ${2}{(8)}{ + 2y = 20}$ $16+2y = 20$ $16{-16} + 2y = 20{-16}$ $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-5x+3y = -34}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 3y = -34}$ ${y = 2}$